Help! ### Understanding Polynomial Functions and Their Zeros: A Detailed Guide#### Definition of Polynomial FunctionSuppose that the polynomial function \( f \) is defined as follows:\[ f(x) = (x - 13)^2 (x - 8)^3 (x + 4)^3 \]#### Identifying Zeros by Their MultiplicityA zero of a polynomial function is a value of \( x \) that makes the function equal to zero. The multiplicity of a zero refers to the number of times that particular zero appears as a solution. **Task:** List each zero of \( f \) according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None."#### Multiplicity Categories1. **Zero(s) of multiplicity one:** - Enter zeros appearing exactly once.2. **Zero(s) of multiplicity two:** - Enter zeros appearing exactly twice.3. **Zero(s) of multiplicity three:** - Enter zeros appearing exactly three times.#### Visual RepresentationA text box is provided for each multiplicity category:- **Zero(s) of multiplicity one:** [ ] - **Zero(s) of multiplicity two:** [ ]- **Zero(s) of multiplicity three:** [ ]Additionally, there is an option to click on "None" if there is no zero for the given multiplicity.#### ExampleGiven the polynomial \( f(x) = (x - 13)^2 (x - 8)^3 (x + 4)^3 \), the zeros and their multiplicities are:- Zero at \( x = 13 \) with multiplicity 2- Zero at \( x = -8 \) with multiplicity 3- Zero at \( x = 4 \) with multiplicity 3These should be entered in their respective categories in the provided text boxes. Remember to thoroughly check your polynomial for all possible zeros and correctly identify their multiplicities for accurate categorization. This structured approach helps in understanding the behavior of polynomial functions and their zeros, which is foundational in algebra and calculus.

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Suppose that the polynomial function fis defined as follows. f(x)=(x-13)²(x-8)³(x+4)³ List each zero of faccording to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with ca Zero(s) of multiplicity one: 0 8 0,0.... Zero(s) of multiplicity two: X 3 Zero(s) of multiplicity three: 0

Suppose that the polynomial function fis defined as follows. f(x)=(x-13)²(x-8)³(x+4)³ List each zero of faccording to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with ca Zero(s) of multiplicity one: 0 8 0,0.... Zero(s) of multiplicity two: X 3 Zero(s) of multiplicity three: 0

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.2: Polynomial Functions

Problem 81E: Maximize volume An open box is to be constructed from a piece of cardboard 20 inches by 24 inches by...

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